A Data Mining Approach for Detecting Collusion in Unproctored Online Exams


J. Langerbein(1), T. Massing(1), J. Klenke(1), N. Reckmann(1), M. Striewe(1),
M. Goedicke(1), C. Hanck(1)


(1) University of Duisburg-Essen; Germany

Setting

  • Data from the Descriptive Statistics course at the University Duisburg-Essen, Germany
  • Exams consist of arithmetical problems, programming tasks in R, and a short essay task
  • Both exams are conducted digitally with the e-assessment system JACK
    • Each student receives different randomized numerical values across all tasks
    • Event logs capture students’ activities, time stamps, and points during the exams for every subtask
  • The test group took the unproctored exam at home during the COVID-19 pandemic
    • The comparison group took a proctored exam in the facilities of the university
Table 1: Overview over the test and comparison group
Comparison Test
Year 18/19 20/21
N 109 151
Style proctocred unprocotored
Total points 60 60
Sub tasks 19 17
Duration 70 70
  • Data cleaning is conducted, removing students with minimal participation or achievement and students with internet problems

Methodology

  • The study utilized an agglomerative (bottom-up) hierarchical clustering algorithm that can be described by following equation:

\[D(s_i, s_{i'}, v_i, v_{i'}) = \frac{1}{h} \sum_{j=1}^h (w_j^P \cdot d_j^P (s_{ij}, s_{i'j}) + w_j^L \cdot d_j^L (v_{ij}, v_{i'j}))\]

  • \(D(s_i, s_{i'}, v_i, v_{i'})\) the global pairwise dissimilarity
  • \(d_j^P(s_{ij}, s_{i'j})\) points dissimilarity for each task \(j\)
  • \(d_j^L(v_{ij}, v_{i'j})\) students event patterns dissimilarity for each task \(j\)
  • \(\displaystyle \sum_{j=1}^h w_j^P + w_j^L =1\) control the influence of each attribute on the global object dissimilarity
  • We reduce the weights for
    • R-tasks, as these tasks have more noise
    • Essay questions, as the comparison on that kind of task are limited
    • Points achieved
  • Dissimilarities in points achieved for each task \(j\)

\[d_j^P(s_{ij}, s_{i'j}) = | s_{ij} - s_{i'j} |\]

  • \(s_{ij}\) denotes the points achieved by student \(i\) in the \(j\)-th subtask

  • Manhatten metric

  • Dissimilarities in the students event patterns (time of submission) for each task \(j\)

\[d_j^L(v_{ij}, v_{i'j}) = \sum_{m=1}^{K=70} | v_{ijm} - v_{i'jm} |\]

  • \(d_j^L(v_{ij}, v_{i'j})\) students event patterns dissimilarity for each task \(j\)
    • Examination is divided into \(m = 1, ... , 70\) time intervals
    • \(v_{ijm}\) denotes the number of answers of student \(i\) for task \(j\) in the \(m\)-th interval
    • Manhatten metric

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Empirical Results

Dendogram produced by average linkage clustering of the unproctored test group (2020/21). <strong> A-F </strong> mark the clusters with the lowest dissimilarity.

Figure 1: Dendogram produced by average linkage clustering of the unproctored test group (2020/21). A-F mark the clusters with the lowest dissimilarity.

  • Figure 1 shows the dendrogram of the test group
    • Overall a lower level of dissimilarity compared to the comparison group
    • Six clusters (A-F) standing out noticeably from the rest of the cohort
Eevent logs and achieved points of the cluster <strong>B</strong> from the test group (2020/21). Above the scatter plot, a bar chart is added to compare the points per subtask.

Figure 2: Eevent logs and achieved points of the cluster B from the test group (2020/21). Above the scatter plot, a bar chart is added to compare the points per subtask.

  • Figure 2 illustrates the individual comparison of achieved points and event logs of the student cluster with the highest similarity
    • Similar time path
    • Same points for each task
Comparison of the normalised distance measures.

Figure 3: Comparison of the normalised distance measures.

  • Figure 3 compares the normalized distributions of the dissimilarity measures between the comparison and test groups
    • Clusters A, B and E standing out

Discussion

  • Three notable clusters (A, B, and E) consisting of two students each
  • Collusion in larger groups are not found
  • These results are also found with other linkage methods and parameter specifications as weightings
  • The approach provides a basis for the examination of clusters based on comparison with a reference group
  • The elevated risk of detection may indeed discourage students from cheating in unproctored exams

Further Research

  • Long-term efficacy of the collusion detection method during exams and its impact on academic integrity and student behavior
  • Refining methods for gathering and analyzing supplementary evidence